In conventional, low-temperature superconductivity (left), so-called Cooper pairing arises from the presence of an electron Fermi sea. In the pseudogap regime of the cuprate superconductors (right), parts of the Fermi sea are “dried out” and the charge-carrier pairing arises through an increase in the strength of the spin-fluctuation pairing interaction as the temperature is lowered. Credit: ORNL
Scientists have used Titan supercomputer at ORNL to simulate cuprates on the path to superconductivity. The team focused on a pivotal juncture on the cuprates’ path called the pseudogap phase, an in-between phase before superconductivity in which cuprates exhibit both insulating and conducting properties.
High-temperature superconductors are materials that can transport electricity with perfect efficiency at or near liquid nitrogen temperatures (-196C) vs conventional superconductors, which operate at near absolute zero (-273.15C). Hyperefficient electricity transmission could revolutionize power grids and electronic devices. That future energy economy, however, is predicated on advancements in the understanding of how high-temperature superconductors work at the microscopic level.
Since this discovery, scientists have been working to develop a theory that explains the essential physics of high-temperature superconductors like copper oxides, called cuprates. A sound theory would not only explain why a material superconducts at high temperatures but also suggest other materials that could be created to superconduct at temperatures closer to room temperature.
At the heart of this mystery is the behavior of high-temperature superconductors’ electrons in their normal state (i.e., before they become superconducting). A team used the Titan supercomputer at ORNL to simulate cuprates on the path to superconductivity. At the pseudogap phase, an in-between phase before superconductivity the conventional pathway to superconductivity is blocked. Maier’s team, however, identified a possible alternative route mediated by the magnetic push-and-pull of cuprates’ electrons.
Simulating a 16-atom cluster, the team measured a strengthening fluctuation of electronic antiferromagnetism where spins of neighboring electrons point in opposite directions (up and down), as the system cooled. The findings add context to scientists’ understanding of the pseudogap and how superconductivity emerges from the phase.
In conventional low-temperature superconductors such as mercury, aluminum, and lead, the explanation for Cooper pairing of electroncs is well understood, ie it arises from the interaction between electrons and a material’s vibrating crystal lattice (phonons). This theory, however, doesn’t seem to apply to cuprates and other high-temperature superconductors, which are more complex in their composition and electronic structure.
Cuprates consist of 2D layers of copper and oxygen. The layers are stacked on top of each other with additional insulating elements in between. To set the stage for superconductivity, trace elements are substituted between copper and oxygen layers to draw out electrons and create “holes,” impurities in electrons’ magnetic ordering that act as charge carriers. At low temperatures, this hole doping, results in the emergence of a pseudogap, a transition marked by electronic stops and starts.
“In a conventional superconductor, the probability of electrons forming Cooper pairs grows as the temperatures decreases,” Maier said. “In cuprates, the pseudogap’s insulating properties disrupt that mechanism. That begs the question, how can pairing arise?” According to the team’s simulations, antiferromagnetic fluctuations of electrons’ own spin is enough to form the glue.
“These spin fluctuations become much stronger as the material cools down,” Maier said. “The interaction is actually very similar to the lattice vibrations, or phonons, in conventional superconductors — except in high-temperature superconductors, the normal state of electrons is not well-defined and the phonon interaction does not become stronger with cooling.”
Maier’s team approached the problem with an application called DCA++, calculating a cluster of atoms using a two-dimensional Hubbard model – a mathematical description of how electrons behave in solid materials. DCA++, ie “dynamical cluster approximation,” relies on a quantum Monte Carlo technique involving repeated random sampling to obtain its results. “This model is very simple – it’s a very short equation – and yet it’s very hard to solve,” Maier said. “The problem is complex because it scales exponentially with the number of electrons in your system and you need a large number of electrons to describe thermodynamic transitions like superconductivity.”
DCA++ maximizes Titan’s hybrid architecture by making use of the GPUs on each of Titan’s 18,688 nodes. In past demonstrations on Titan, DCA++ has topped 15 petaflops. Furthermore, the DCA algorithm minimizes a common problem associated with calculating many-particle systems using the Monte Carlo method, the fermionic sign problem.
In physics, the quantum nature of electrons and other fermions is described by a wave function, which can switch from positive to negative – or vice versa – when 2 particles are interchanged. When the positive and negative values nearly cancel each other out, accurately calculating the many-particle states of electrons becomes tricky.
“The sign problem is affected by cluster size, temperature, and the strength of the interactions between the electrons,” Maier said. “The problem increases exponentially, and there’s no computer big enough to solve it. What you can do to get around this is measure physical observables using many, many processors. That’s what Titan is good for.”
DCA++ works by measuring notable physical characteristics of the model as it walks randomly through the space of electronic configurations. Running on Titan, the code allows for larger clusters of atoms at lower temperatures, providing a more complete snapshot of the pseudogap phase than previously achieved.
Moving forward, Maier’s team is focused on simulating more complex and realistic cuprate systems to study the transition temperature at which they become superconducting, a point that can vary greatly within the copper-oxide family of materials. To take the next step, the team will need to use models with more degrees of freedom, or energy states, information that must be derived from first-principles calculations that take into account all the electrons and atoms in a system.
“Once we get that, we can ask why the transition temperature is higher in one material and lower in another,” Maier said. “If you can answer that, you could do the same for any high-temperature superconductor or any material you want to simulate.” http://www.newswise.com/articles/titan-shines-light-on-high-temperature-superconductor-pathway
http://www.nature.com/ncomms/2016/160617/ncomms11875/full/ncomms11875.html
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